Hi Curtis,

I need some help with percent and ratio word problems. Unfortunately your previous explanations regarding word problems have been too complicated. Perhaps you could give more information on the basics, the formulas? I know I am not completely understanding these formulas. My knowledge in math is only the basic concepts, and I do not understand algebra yet.

While percents seem simple enough; I become lost when I try to solve word problems with them. I have been using the triangle method to work with percent problems. [The method shown in the GED book.]

1- Multiply when the problem gives you the whole and the percent.

2- Divide when the problem gives you the part and the percent.

3- Divide when the problem gives you the whole and the part.

However, I am still finding word problems with percents and ratios very confusing, so I know I am definitely not understanding the formula. Ratios especially – the whole idea of cross multiplying sounds good, but when I do this I become lost as I attempt to finish the problem. I hope you can help me begin to make sense of these areas.

Thanks, Jen

Hey, Jen. The problem with percent and ratio word problems is, you gotta really think through what information they give you an’ how it relates to the problem they want you to solve. What are you actually tryin’ to find? How can you get it? It’s knowing when to use the different rules and formula’s that’s confusin’.

Like the triangle rules you said you use:

1- Multiply when the problem gives you the whole and the percent.

2- Divide when the problem gives you the part and the percent.

3- Divide when the problem gives you the whole and the part.

To use ‘em, you gotta know what ‘percent’ ‘whole’ an’ ‘part’ they mean. Here’s an example.

40 of the students in a class of 200 got B’s on their test. 10 got A’s, 2 got F’s, and 20 got D’s. What percentage of students got C’s?

What’s the whole, part, and percent?

The whole is the whole class: 200.

The percent is the percent of students got C’s. That’s what you’re looking for.

The “part” is the number of students that got C’s.

See, a “percent” is the fraction (or ratio) of the part to the whole. That’s all… it’s just a fraction, with the top divided by the bottom. So, 1/2 = 50% (1 divided by 2 = .5 = 50%) and 3/4 = 75% (3 divided by 4 = .75 = 75%). The part divided by the whole = the percent.

Part ÷ Whole = Percent

So, in a sense, a percent is the same thing as a fraction. 1/8 of a pizza is the part (1 piece) over the whole (8 pieces make a whole pizza). That same slice of pizza is 12.5% of the pizza, because 1 divided by 8 = .125 (12.5%).

All three of the “rules” come from the equation: Part ÷ Whole = Percent, just written in different ways.

1- Multiply when the problem gives you the whole and the percent. (Part = Percent x Whole)

2- Divide when the problem gives you the part and the percent. (Whole = Part ÷ Percent)

3- Divide when the problem gives you the whole and the part. (Percent = Part ÷ Whole)

All these formulas say the same thing… it’s just moving the three pieces of the formula around. So really, all you need to do is figure out what the question’s askin’, and find the other two numbers to plug into the formula.

Back to the word problem. It’s asking for a percent:

Percent = Part ÷ Whole

The “whole” is the whole class, 200 students.

Percent = Part ÷ 200

The “part” is trickier, cuz the word problem is really in 2 parts. The “part” is the number of students that got c’s. So, you need to subtract all the other students who got other grades from 200.

200 – 40 – 10 – 2 – 20 = 128

That’s the number to plug into the formula:

Percent = 128 (number of students with C’s) ÷ 200 (number of students in the class)

128 ÷ 200 = .64 = 64%

64% of students got C’s.

Okay, let’s try a ratio. A ratio is also sort of like a fraction, but it’s not necessarily the ratio of “part” to “whole.” A fraction is a ratio of “part” to “whole,” but a ratio is a ratio of anything to anything. In a speed problem, it can be a ratio of “miles” to “hours.” It’s anything that has a regular relationship. Okay, let’s try a ratio problem, and we’ll try an’ walk thru cross-multiplying.

A man works 8 hours per day in a factory, and he makes $20 per hour. In a 5-day workweek, how much does the man make?

Now, you might figure this out without even using a ratio. But it is a ratio… any time you see “per,” you can use a ratio. You need to figure out what’s equivalent to what. We’ve got some ratios:

8 hours : 1 day

That’s the same as 8 hours per day.

20 dollars : 1 hour

That’s the same as $20 per hour.

Now, if I want to find out how many dollars per day, I need to figure out the ratio of dollars to 8 hours. A ratio like this (something per something else) gives two things that are equivalent. 8 hours = 1 day, so a ratio of dollars per 8 hours will give us dollars per day.

20 dollars : 1 hour

x dollars : 8 hours

Now, I’ve got two ratios, with the same units, and they’ll be equal to each other. That gives me an equation:

20/1 = x/8

Now’s the time to cross multiply. Basically, cross multiplication is some simple algebra. It’s just a shorthand way to remember how to solve this kind of problem. To move numbers from one side of the equation to the other, you do the opposite operation. If one side is divided by a number (like 1), you can move that number to the other side of the equation by multiplying both sides by 1.

(20/1) x 1 = (x/8) x 1

The two ones on the left cancel each other out, and on the right you end up with x times 1 (or just x) over 8:

20 = x/8

Now, do the same thing with the 8:

20 x 8 = (x/8) x 8

The two 8’s cancel each other out, and 20 x 8 = 160:

160 = x

He makes $160 in a day.

160 dollars : 1 day

Now, how much does he make in 5 days?

y dollars : 5 days

It’s the exact same sort of problem. You can make an equation:

160/1 = y/5

Using the shorthand version of the math we did before, this is the same as 160 x 5 = 1 x y (cross multiplying)

160 x 5 = 1 x y

800 = y

That’s the answer: he makes $800 in a five-day workweek.

So, what you need to find out from a ratio problem is what ratio equals what other ratio. Then, you can cross-multiply to solve.

Hope this helps! If a practice problem is giving you problems, send it to me an’ I’ll walk thru it.

For more information about the GED test and GED test preparation, visit The GED Academy at http://www.passGED.com.

Jesse writes:I was wondering If u could let me know if I got these two questions correct I’m taking my ged next week & I want to feel comfortable with this math.
On a map 1/3 in=15 miles find the distance between two towns on a map that equals 3 2/3 in. How many miles r between the two? my answer was 75 miles am I correct?Next Question

The scale on a map indicates that 1/2 inch represents an actual distance of 120 miles, how far apart will two towns be if the actual distance between them is 180 miles my answer was 2 inches am I correct? if not could u explain how to set up these type of problems? thank you, Jesse.

Jesse,

Hey! Congrats on your GED test comin’ up. Y’know what these questions are? Ratios. I got a ratio post on my blog at: http://www.passged.com/student_blogs/curtis/2007/12/24/rice-ratios-gotta-love-that-ged-math/

There’ll prolly be a ratio question on the GED test. Here’s how it works. Take the first question. You got 1/3 inch, that equals 15 miles. Picture it in your head. Say this line is 1/3 inch: |—| It be 15 miles.

So, you got to find out how many miles in 3-2/3 inch. Well, first you gotta find out, how many 1/3-inches are in 3-2/3 inch. Get it?

Three 1/3-inch lengths are in 1 inch, like this:
|—|—|—|

So, in 3-2/3 inches, there’s 11 1/3-inch lengths:
|—|—|—|
|—|—|—|
|—|—|—|
|—|—|

Each 1/3-inch is 15 miles, right? So, we got 11 lengths of 15 miles… that’s 15 times 11, and that’s 165 miles! There ya go. Always makes it easier to understand to picture it in your head.

If you want to do it mathematically, what I did was set up a ratio:
1/3:15
3-2/3:x

Divide 3-2/3 by 1/3… then multiply 15 by the answer to get x.

Here’s the other one.
1/2 inch = 120 miles
x = 180 miles

Same deal here, right? You got a ratio.
1/2 inch:120 miles
x:180 miles

The relationship between 120 and 180 got to be the same as between 1/2 and the answer. So, what’s the relationship between 120 and 180? If you divide 180 by 120, 180/120 = 18/12 = 9/6 = 3/2 = 1-1/2

So, 180 is 1-1/2 times 120. Then x got to be 1-1/2 times 1/2. That’s 3/4. If it’s easier, you can do 1.5 x .5 = .75 …same thing. So, the answer’s 3/4 inch. Get it?

Hope this helps!

Curtis

For more information about the GED test and GED test preparation, visit The GED Academy at http://www.passged.com.

If this was a GED question, it’s be a breeze. If I got 1-1/2 coffee mugs of rice, and I need a 1:2 ratio of rice to water, then I need 3 coffee mugs of water.

If I had 3/4 coffee mugs of rice, I’d need 1-1/4 of water, or (2) 3/4 coffee mugs. Get it?

If I had 2-2/3 coffee mugs of rice, I’d need 5-1/3 (4 + 4/3) coffee mugs of water.

Pretty easy. A 1:2 ratio means the second thing’s always 2 times the first thing. I know you’ve got ratios totally down, now, so if you see any on the GED test, you’ll know what to do.
And the recipe works pretty good, too. I just put 1-1/2 coffee mugs of rice and 3 coffee mugs of water in a big bowl, nuke them for 10 minutes, turn it down to 50% and nuke ‘em for 15-20 minutes. Then, bingo, I got rice.

Don’t worry, I ain’t gonna start cooking all the time.

Next time, let’s get back to these elections that’s comin’ up… I wanna start applyin’ some of that GED math to some real important real life… Because the GED test is pretty important, but so’s the real world, like the elections, right?

To find out more about the GED test and GED test preparation, visit The GED Academy at passGED.com.

Well, she taught me a quick and easy way to make some rice in the microwave. Cheap way to eat. She gave me a bunch of measurements, but I don’t have no measuring cups. So she put it in terms of a ratio… you gotta have a 1:2 ratio of rice to water.

Well, I’ve got a coffee mug to measure stuff with, that’s it. Here’s the question…

I’ve got 1-1/2 coffee mugs worth of rice. How much water do I got to have to cook this stuff? Does the 1:2 ratio give me enough information?